Most discussions of a pion condensate use a nonlinear Lagrangian, in which the \(\sigma \)  meson does not explicitly appear.
The advantage of using a linear Lagrangian is that it is much easier studying how the symmetric phase is approached.
Following Ref. [1]} I
generalize from \(O(4)\)  to \(O(N)\) , where the solution is direct as \(N \rightarrow \infty \)  [2]}, [3]}.
